consider the following optimization problems:
1. maximize f(x,y) subject to x-2y=1 and 3x+2y=11
2.minimize f(x,y) subject to x-2y=1 and 3x+2y=11
which of the following is true?
a. the 2 problems have the same solution
b. the solutions to the 2 problems are different
c. neither of the problems has a solution
d. nothing can be said about the solutions of the problems unless the objective function is completely specified
The two problems have the same solution because the two constraints have only 1 intersection point say P= (x*,y*).
In this case we are optimizing the function f(x,y) with a feasible constraint set, which is just a
single point P.
Masters in Economics
Delhi School of Economics